The invention is based on a method for injecting fuel into the combustion chambers of an air-compressing, self-igniting internal combustion engine. In one such method, known from European Patent Disclosure EP-A1 0 621 400, a postinjection of fuel after the main injection, in conjunction with an exhaust gas post treatment device, is proposed with the goal of reducing the NO.sub.x components in the exhaust gas. A so-called deNO.sub.x catalytic converter is provided as the post-treatment device, which in combination with highly reactive hydrocarbon fragments in the exhaust gas is intended to bring about a reduction of the NO.sub.x components. This reduction is efficient in particular only whenever still uncombusted hydrocarbons enter the catalytic converter. To that end, in particular, a late postinjection is employed, which occurs at a crankshaft angle of 80.degree. after top dead center; although the fuel is not combusted, nevertheless because of the residual heat it is optimally prepared by being evaporated or cracked. The hydrocarbon molecules thus produced can then subsequently bring about an optimal NO.sub.x conversion in the catalytic converter. However, this fuel injection is not active or effective until the operating temperature of the catalytic converter or the exhaust gas temperature is sufficiently high. For an operating range in which this optimal exhaust gas temperature has not yet been reached, it is also proposed that an early postinjection be performed, which is intended to be in the range between 20.degree. and 80.degree. of crankshaft angle after top dead center. This injection takes place whenever the combustion of the fuel quantity introduced via the main injection has at least largely ended. The fuel quantity injected thereafter via the postinjection is intended then to combust as completely as possible, for the sake of heating up to the exhaust gas temperature and bringing the catalytic converter to the desired temperature. Once that has been done, the postinjection proceeds as noted above.
Along with the goal of reducing NO.sub.x emissions, however, in Diesel engines there is also the need with regard to exhaust gas emissions to keep the soot components in the exhaust gas low. The known method provides no points of departure for achieving this. Beyond the goal of reducing soot emissions, there is also the goal, in the sense of optimizing a Diesel injection system, of keeping the specific fuel consumption and noise low.